5.2.5 Addition and Subtraction on the Number Line
The number line can be used to show how calculations can be carried out with negative numbers. First check how this works with positive numbers by looking at the sum .
Start at 2 and move 4 units to the right (because you are adding a positive number) to get the answer 6.
The same method works if the starting number is negative. For example, suppose you are in debt by $5, so your account balance is recorded as −$5. If you then pay $8 into your account, $5 of this will pay off your debt and $3 will be recorded as your new balance, so .
On the number line, the starting number is −5, and moving 8 units to the right verifies the answer as 3.
Now consider subtraction, for example . Here, the starting number is 6, but this time we move 4 units to the left to get to the answer, which is 2.
Similarly, if your account is overdrawn by $2, and then you withdraw another $3, your account will be overdrawn by $5. This is represented on the number line by starting at −2, then moving 3 units to the left to get the answer −5. This is written as .